From Bangkok you can fly to either the Phuket Intenational Airport or the smaller Krabi Airport. Check availability and prices on Bangkok Airways and Nok Air. Both fly direct into Krabi and Phuket 3 or 4 times daily depending on high season or not. If you book online with these airlines, read the fine print before you book because in some cases you are able to book all inclusive flights where the price also includes the shuttle bus service from the Phuket Airport to the Rassada Pier and the boat transfer from the Rassada Pier in Phuket to the Tonsay Pier on Koh Phi Phi.
Alternatively, you can rely upon http://www.phuketferryboats.com/ they have a comprehensive ferry schedule on their website and they can do private airport picks up or join up airport picks. You can book online, pay by PayPal, it all works, the service is good and the cars or shuttles are new. Write down their phone number and call them after you arrive with your Thai cell phone. 086-942-8733. Or email them the day before at email@example.com. We paid $89 for a private car transfer from Phuket Airport to the Rassada Pier and this price also included our return private car transfer 4 days later as well as the 2 way Ferry transfer costs to and from Koh Phi Phi.